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Issue ESAIM: PROC
Volume 18, 2007
Paris-sud working group on modelling and scientific computing 2006-2007
Page(s) 216 - 228
DOI 10.1051/proc:071816
Published online 12 September 2007

ESAIM: Proc., 2007, Vol. 18, pp. 216-228
DOI: 10.1051/proc:071816

Transformée en Ondelettes Continue Directionnelle : applications en Imagerie Médicale

Valérie Perrier1, Anne Bilgot2, Olivier Le Cadet1 and Laurent Desbat2

1  Laboratoire Jean Kuntzmann, Institut National Polytechnique de Grenoble, BP 53, 38041 Grenoble Cedex 9
2  Laboratoire de Techniques de l'Imagerie, de la Modélisation et de la Cognition de l'IMAG, Institut de l'Ingénierie de l'Information de Santé, Faculté de Médecine, Domaine de la Merci, 38706 La Tronche


(Février 2007 / Published online: 12 September 2007)

Abstract
This article comes from a short lecture given at the Graduate School of Paris Orsay's university during December, 2005. We present the directional continuous wavelet transform in dimension 2, and the general associated synthesis formula. We develop two fundamental examples of wavelets in image processing, and propose a practical method for the coefficients calculation. We illustrate this theory by two original applications in medical imaging, related to reconstruction of objects from incomplete data: local tomography and the identification of a vertebra surface from two X-ray images.


Résumé
Cet article est issu d'un mini-cours donné à l'école doctorale de l'université d'Orsay en décembre 2005. Nous présentons la transformée en ondelettes continue directionnelle en dimension 2, et la formule de synthèse générale associée. Nous insistons sur deux exemples fondamentaux d'ondelettes en traitement d'image, et proposons un calcul pratique des coefficients. Nous illustrons ensuite cette théorie par deux applications nouvelles en imagerie médicale, liées à des problèmes de reconstruction d'objets à partir de données incomplètes : la tomographie locale, et l'identification d'une surface de vertèbre à partir de deux radiographies.


Mathematics Subject Classification. 42C40, 68U10

Key words: Transformée en ondelettes, imagerie médicale, transformée de Radon, segmentation d'images


© EDP Sciences, ESAIM 2007


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